Ok, after some fiddling around I got to a working solution. I downloaded phpunit-lts.phar from phpunit.de and put it directly into the project (along with the other files... meh).
Do not use the most current version (4.0 as of 21st of march 2014) of PHPUnit! Versions beyond 3.7 (or 3.8, as it seems) are not supported by IDEA or PHPStorm. You will get
PHP Fatal error: Class IDE_PHPUnit_Framework_TestListener contains 1 abstract method and must therefore be declared abstract or implement the remaining methods (PHPUnit_Framework_TestListener::addRiskyTest) in /tmp/ide-phpunit.php on line 504
So do yourself a favor and stick to the LTS version for now.